And there's the lone CP of the map. But two CP squares in the HUD? How does that work?

Like this. As opposed to traditional attack/defend, an enemy being on a neutral CP doesn't speed up their CP decay. All you've got to do is get in the cage, and try to hold it for as long as you can, capping "your" CP before they cap "theirs"

Of course, what's a map without SNIPAN GAEMS? Note how the smaller secondary spawn is shielded from snippers